Hello, I grew up reading the Young Wizards series and it shaped a lot of who I am as a person now. I was just wondering why you chose the specific knot you did for the wizards knot?
Well, for one thing it's mathematically interesting.
...Maybe this is the wrong end of the story to start from. (Though it is mathematically interesting...)
Early references to the Wizard's Knot in the books describe "a complicated sort of figure-eight mark". It takes a number of other forms as the series goes on, and I started to realize that I was going to have to nail the thing down more concretely... in some way that would allow it to exist both in a very simple form, and in versions more complex.
So the question "how is a complicated symbol also a simple one (or vice versa, depending on which you need)?" can only sensibly be answered in one cognitive realm: topology—specifically, the corner of that science known as knot theory.
It would be possible for me to go on at serious length about this, but probably (especially this late at night...) it's best for everybody if I don't get started. Briefly, though: I looked around the world of knots for a while and eventually found that the knot called the 7-4 knot was what I needed. It appears in numerous Earth-based cultures as “the Endless Knot” in an assortment of interesting forms, and it has a nice symmetry in all of them. But most importantly, its simplest forms can be written with a single long stroke of the pen* (or wand, if you're one of those YoungWizards-verse wizards who choose to use wands), just as that simplest figure-eight(ish) form.
Now, a perfect or exact congruency between these has to be come at by sort of (mathematically) squinting at both of them at once, sideways. But there often comes a time when, if you're the storyteller, you decide that you've come (as we say around here) "close enough for jazz"... and with a sigh you step away from the final resolution of a conundrum like this to deal with more important issues. Like plot. :)
...So there you have it. Hope this helps!